Driver: Scripted Expression (Copy and invert some Objects Rotation and apply it to another Object)
Scripted expression expects a mathematical function using the variable you set underneath (default name is "var", but you can choose your own, avoiding blank spaces or others special sign).

In this example I've set the Z rotation of the child object to be driven by Z rotation of the parent Obj. The name of the variable is "var_ob_par", and the scripted expression is " - var_ob_par".

It works!